13 citations · 15 across the 4 of their papers we have counts for
5 papers
Non-degenerate minimal submanifolds as energy concentration sets: a variational approach
Guido De Philippis, Alessandro Pigati
We prove that every non-degenerate minimal submanifold of codimension two can be obtained as the energy concentration set of a family of critical maps for the (rescaled) Ginzburg-L…
Convergence of the self-dual -Yang-Mills-Higgs energies to the -area functional
Davide Parise, Alessandro Pigati, Daniel Stern
Given a hermitian line bundle on a closed Riemannian manifold , the self-dual Yang-Mills-Higgs energies are a natural family of functionals \begin{align*} &E_ε(u,…
The viscosity method for min-max free boundary minimal surfaces
Alessandro Pigati
We adapt the viscosity method introduced by Rivière to the free boundary case. Namely, given a compact oriented surface , possibly with boundary, a closed ambient Riemannian man…
Minimal submanifolds from the abelian Higgs model
Alessandro Pigati, Daniel Stern
Given a Hermitian line bundle over a closed, oriented Riemannian manifold , we study the asymptotic behavior, as , of couples critical for the…
Free boundary minimal surfaces: a nonlocal approach
Alessandro Pigati, Francesca Da Lio
Given a -smooth closed embedded manifold , with , and a compact connected smooth Riemannian surface with $\partial S\neq\emptys…